A necessary and sufficient condition for the perspective observability problem

A generalized Popov-Belevitch-Hautus test of observability

“…Note that for almost every point on the image plane, (1.10) describes a homogeneous seven-dimensional plane in R9. Thus if one observes ( i l l , 6 2 , 1 1 1 . 712) for 3 points on the image plane, the output vector in (1.11) is observed up to a homogeneous 3-plane.…”

“…The above class of problem occurs in machine vision as has already been introduced in [6], [I]. Specifically if we consider a plane in R3 with coordinates (.Ti, Er.…”

State estimation and control for systems with perspective outputs

“…It should be noted that for perspective linear systems without inputs it is never possible to recover the norm of the state because the system is homogeneous on the initial conditions. Therefore Dayawansa et al [4] only consider state indistinguishability up a homogeneous scaling of the state. However, as shown in [7], for perspective systems with inputs it is in principle possible to recover the whole state from projective outputs.…”

“…In the last few years, the observability of perspective linear systems has been systematically studied in the literature and [4] provides an elegant algebraic observability test. It should be noted that for perspective linear systems without inputs it is never possible to recover the norm of the state because the system is homogeneous on the initial conditions.…”

State Estimation for Systems with Implicit Outputs for the Integration of Vision and Inertial Sensors

“…The reader is referred to [2], [3] for several other examples of perspective systems in the context of motion and shape estimation. See also [4], [5] that address the observability problem of perspective linear systems. The system with implicitly defined outputs described in [6] and the state-affine systems with multiple perspective outputs considered in [7] (see also [8]- [10]) are also special cases of (1)- (3).…”